Simplify the following expression: $ x = \dfrac{-5}{z - 3} + \dfrac{-8}{9} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{-5}{z - 3} \times \dfrac{9}{9} = \dfrac{-45}{9z - 27} $ Multiply the second expression by $\dfrac{z - 3}{z - 3}$ $ \dfrac{-8}{9} \times \dfrac{z - 3}{z - 3} = \dfrac{-8z + 24}{9z - 27} $ Therefore $ x = \dfrac{-45}{9z - 27} + \dfrac{-8z + 24}{9z - 27} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-45 - 8z + 24}{9z - 27} $ $x = \dfrac{-8z - 21}{9z - 27}$